# Questions tagged [profile-likelihood]

The profile likelihood function is an inference function constructed from the likelihood function. If the likelihood function depends on many parameters and only some are of interest, then the other parameters are removed "by concentration", which means that they are "maxed out".

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### One sided likelihood ratio test for a logistic regression model?

I need to run a one-sided test on one parameter of a logistic regression model: $H_0$: $\beta = 0$ $H_1$: $\beta \geq 0$ I want to avoid Wald-equivalent methods as these are known to have problems ...
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### How to make the profile likelihood model for estimation?

I tried to make the age estimation model using the chemical compound results from The soil. Initially, I used the multivariable regression model. However, the reviewer highly recommend using the ...
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### Grid search for estimation of degrees of freedom parameters in likelihood function

In the script below I attempt to estimate parameters for Apple and Amazon using a Gaussian Copula with t-Student marginals for the purpose of this exercice. When executing the script, I notice at each ...
37 views

### Profile (quasi-)likelihood score tests

Suppose I have a log-likelihood or quasi-log-likelihood for my data in terms of the parameter vectors $\theta$ and $\psi$: $$L(\theta;\psi)=\frac{1}{T}\sum_{t=1}^T{\log{f(y_t|\theta;\psi)}}.$$ (I am ...
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1 vote
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### Profile likelihood vs quadratic log-likelihood approximation

I want to compare two alternative approaches for evaluating the uncertainty of the multi-dimensional MLE $\widehat \theta$ based on a log-likelihood function $l$: Compute a Fisher-information-based ...
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### Approximating profile likelihood confidence intervals when I only have a score function and not a likelihood

I'm working on a modeling problem where I can define a score function that looks a lot like a binomial likelihood, but the model isn't really binomial. I'd like to use profile likelihood to estimate ...
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### Confidence intervals for GLMM: bootstrap vs likelihood profile

I've built a relatively large negative binomial GLMM (~50000 observations, 10 covariates in conditional model, 1 covariate as zero-inflation model, 3 random intercepts (650, 26, 26 levels in each ...
• 380
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### In a GLM, are the Maximum likelihood estimators for the regression coefficients always normally distributed?

I'm doing a Poisson regression and using the confint function in R to generate confidence intervals for my regression coefficient. These result in different ...
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### Is the profile likelihood (dependent on one parameter) always a concave function?

Let $\theta = (\theta_1, \theta_2, \dots)$ be a vector of parameters, and let $L(\theta) = L(\theta|y)$ denote the likelihood function with respect to observed data $y$. Following the notation from ...
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### Confidence interval on the percentage difference of two binomial distributions

I have survey data for women and men following a binomial distribution. Their means are $p_1$ and $p_2$ respectively. I have calculated $(p_1-p_2)/p_2$ and would like to attach a confidence interval ...
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### Is my explanation of profile likelihood plots correct?

Using the metafor package in R to conduct a mixed-effects meta-analysis and meta-regression, I checked the profile likelihood ...
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### Confidence intervals with penalized likelihood

I am trying to perform parameter estimation using something like a maximum likelihood ratio method, however I need to add a penalty term to constrain nuisance parameters which describe certain ...
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### Firth's method for logistic regression - interpretation of R output

I have a multivariate, multinomial logistic regression model with exclusively continuous covariates. After some examination, I found that I had a problem of quasi-complete separation. The textbook ...
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### Constructing likelihood for a statistical functional

I'm a bit confused about something that I've seen in several engineering papers. Suppose we have a random variable $X$ with unknown distribution $p(x)$. We're interested in the value of a ...
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I am aiming to show that the MLE of $(\alpha, \lambda)$ for $X_1, \dots, X_n \sim \Gamma(\alpha,\lambda)$ exists and is unique, under the assumption that the $X_i$ are all positive and unequal. I am ...